It has been known that simply mixing single-walled carbon nanotubes (SWCNTs) in an aqueous solution of gelatin disperses SWCNTs well for a period of months. Gels made from the gelatin-SWCNT mixture are also stable and have a clear, black color. Scanning electron microscopy shows that gelatin molecules self-organize into a foamlike structure. All SWCNTs are embedded in the gelatin film that makes up the foam walls. Those SWCNTs belonging to one face of the foam cell cannot approach other faces to make van der Waals contact. Thus, the foam structure is associated with stabilization of the SWCNT dispersion. The gelatin can be removed thermally while maintaining the foam structure to give a sponge made of nanotube foams. This highly porous solid is electrically conducting and mechanically stable and can be used as a structural frame for composite materials.